That seems very strange. Can you cite a reference so we can see exactly what "they in the International Style" say? I learned American Style first, but for several years I took lessons from an instructor who taught only International, and I never heard him say anything like that. In fact, many times he said things like "How do I get her to do ___? Because I lead it."

In Foxtrot (American or International), for example, if I step forward on my left foot while beginning to turn left, I might be starting any of several figures. My partner can't just do the steps because she knows what's coming next (and if she's simply doing memorized steps we aren't dancing together). I have to communicate to her what's coming next. I have to be able to lead, and she has to be able to follow (which in my opinion is harder).

While thinking of how to dance the pattern being danced, the leader also has to think of what pattern will follow it, and also has to be aware of other couples on the floor. And did I mention listening to the music? Whether that is actually thinking of two (or more) things at the same time is a subject for those who study how the brain works, but that's what you have to do.